A072960 -id:A072960 - cp's OEIS frontend

A028374 Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}.

0, 2, 3, 5, 6, 8, 9, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 50, 52, 53, 55, 56, 58, 59, 60, 62, 63, 65, 66, 68, 69, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 200, 202, 203, 205, 206, 208, 209, 220, 222, 223, 225, 226, 228, 229, 230, 232, 233

Offset: 1

Greg Heil (gheil(AT)scn.org), Dec 11 1999

From Bernard Schott, Mar 26 2023: (Start)
Previous name was: "Curved numbers: numbers that have only curved digits (0, 2, 3, 5, 6, 8, 9)"; but in fact, the curved numbers form the sequence A072960.
This sequence allows all digits except for 1, 4 and 7. (End)

			From _K. D. Bajpai_, Sep 07 2014: (Start)
206 is in the sequence because it has only curved digits 2, 0 and 6.
208 is in the sequence because it has only curved digits 2, 0 and 8.
2035689 is the smallest number having all the curved digits.
(End)

K. D. Bajpai, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A028373 (straight digits: 1, 4, 7), A072960 (curved digits: 0, 3, 6, 8, 9), A072961 (both straight and curved digits: 2, 5).
Combinations: A082741 (digits: 1, 2, 4, 5, 7), A361780 (digits: 0, 1, 3, 4, 6, 7, 8, 9).
Cf. A034470 (subsequence of primes).

[n: n in [0..300] | Set(Intseq(n)) subset [0,2,3,5, 6,8,9] ]; // Vincenzo Librandi, Sep 19 2014

N:= 3: S:= {0, 2, 3, 5, 6, 8, 9}: K:= S:
for j from 2 to N do
     K:= map(t -> seq(10*t+s, s=S), K);
         od:
print( K);  # K. D. Bajpai, Sep 07 2014

f[n_] := Block[{id = IntegerDigits[n], curve = {0, 2, 3, 5, 6, 8, 9}}, If[ Union[ Join[id, curve]] == curve, True, False]]; Select[ Range[0, 240], f[ # ] & ]
Select[Range[0, 249], Union[DigitCount[#] * {1, 0, 0, 1, 0, 0, 1, 0, 0, 0}] == {0} &] (* Alonso del Arte, May 23 2014 *)
Select[Range[0,500],Intersection[IntegerDigits[#],{1,4,7}]=={}&] (* K. D. Bajpai, Sep 07 2014 *)

for n in range(10**3):
  s = str(n)
  if not (s.count('1') + s.count('4') + s.count('7')):
    print(n,end=', ') # Derek Orr, Sep 19 2014

Corrected and extended by Rick L. Shepherd, May 21 2003
Offset corrected by Arkadiusz Wesolowski, Aug 15 2011
Definition clarified by Bernard Schott, Mar 25 2023

A034470 Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9.

Original entry on oeis.org

2, 3, 5, 23, 29, 53, 59, 83, 89, 223, 229, 233, 239, 263, 269, 283, 293, 353, 359, 383, 389, 503, 509, 523, 563, 569, 593, 599, 653, 659, 683, 809, 823, 829, 839, 853, 859, 863, 883, 929, 953, 983, 2003, 2029, 2039, 2053, 2063, 2069, 2083, 2089, 2099, 2203

Offset: 1

Robert G. Wilson v, Jan 24 2003

Intersection of A000040 and A028374. - K. D. Bajpai, Sep 07 2014

			From _K. D. Bajpai_, Sep 07 2014: (Start)
29 is prime and is composed only of the curved digits 2 and 9.
359 is prime and is composed only of the curved digits 3, 5 and 9.
(End)
20235869 is the smallest instance using all curved digits. - _Michel Marcus_, Sep 07 2014

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A028374, A072960, A079652.

N:= 4: # to get all entries with at most N digits
S:= {0,2,3,5,6,8,9}:
T:= S:
for j from 2 to N do
T:= map(t -> seq(10*t+s,s=S),T);
od:
select(isprime,T);
# In Maple 11 and earlier, uncomment the next line:
# sort(convert(%,list)); # Robert Israel, Sep 07 2014

Select[Range[2222], PrimeQ[#] && Union[Join[IntegerDigits[#], {0, 2, 3, 5, 6, 8, 9}]] == {0, 2, 3, 5, 6, 8, 9} &] (* RGWv *)
Select[Prime[Range[500]], Intersection[IntegerDigits[#], {1, 4, 7}] == {} &] (* K. D. Bajpai, Sep 07 2014 *)

A079652 Prime numbers using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

3, 83, 89, 383, 389, 683, 809, 839, 863, 883, 983, 3083, 3089, 3389, 3803, 3833, 3863, 3889, 3989, 6089, 6389, 6689, 6803, 6833, 6863, 6869, 6883, 6899, 6983, 8009, 8039, 8069, 8089, 8093, 8363, 8369, 8389, 8609, 8663, 8669, 8689, 8693, 8699, 8803, 8839

Offset: 1

Shyam Sunder Gupta, Jan 23 2003

Intersection of A000040 and A072960. - K. D. Bajpai, Sep 01 2014

K. D. Bajpai, Table of n, a(n) for n = 1..11740
Chris K. Caldwell and G. L. Honaker, Jr., 30689, Prime Curios!
Chris K. Caldwell and G. L. Honaker, Jr., 90863, Prime Curios!

Cf. A072960, A028374.

Cf. A034470.

N:= 4: # to get all terms with up to N digits
Digs:= {0,3,6,8,9}:
A:= NULL:
for d from 1 to N do
  C:= combinat[cartprod]([Digs minus {0},Digs $(d-1)]);
  while not C[finished] do
    L:= C[nextvalue]();
    x:= add(L[i]*10^(d-i),i=1..d);
    if isprime(x) then A:= A,x fi
  od
od:
A; # Robert Israel, Aug 31 2014

Select[ Range[8850], PrimeQ[ # ] && Union[ Join[ IntegerDigits[ # ], {0, 3, 6, 8, 9}]] == {0, 3, 6, 8, 9} &]
Select[Prime[Range[5000]], Intersection[IntegerDigits[#], {1, 2, 4, 5, 7}] == {} &] (* K. D. Bajpai, Sep 01 2014 *)
Select[FromDigits/@Tuples[{0,3,6,8,9},4],PrimeQ] (* Harvey P. Dale, Sep 05 2022 *)

A082741 Numbers that have digits consisting only of line segments or both line segments and curves (base 10 digits are 1, 2, 4, 5, 7).

Original entry on oeis.org

1, 2, 4, 5, 7, 11, 12, 14, 15, 17, 21, 22, 24, 25, 27, 41, 42, 44, 45, 47, 51, 52, 54, 55, 57, 71, 72, 74, 75, 77, 111, 112, 114, 115, 117, 121, 122, 124, 125, 127, 141, 142, 144, 145, 147, 151, 152, 154, 155, 157, 171, 172, 174, 175, 177, 211, 212, 214, 215, 217, 221

Offset: 1

Rick L. Shepherd, May 21 2003

This sequence allows the digits 2 and 5, formed from combinations of line segments and curves; the subsequence A028373 does not.

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for 10-automatic sequences.

Cf. A028373 (line-segment digits 1, 4, 7 only), A028374 (digits with curves or both curves and line segments), A072960 (curved digits 0, 3, 6, 8, 9 only).

a:= proc(n) local d, i, m, r; m:=n; r:=0;
      for i from 0 while m>0 do
        d:= irem(m, 5, 'm');
        if d=0 then d:=5; m:=m-1 fi;
        r:= r+10^i*[1, 2, 4, 5, 7][d]
      od: r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 25 2014

Table[FromDigits/@Tuples[{1,2,4,5,7},n],{n,3}]//Flatten (* Harvey P. Dale, Apr 17 2022 *)

A214584 Integers whose decimal representation has only digits in {4,5,7}.

Original entry on oeis.org

4, 5, 7, 44, 45, 47, 54, 55, 57, 74, 75, 77, 444, 445, 447, 454, 455, 457, 474, 475, 477, 544, 545, 547, 554, 555, 557, 574, 575, 577, 744, 745, 747, 754, 755, 757, 774, 775, 777, 4444, 4445, 4447, 4454, 4455, 4457, 4474, 4475, 4477, 4544, 4545, 4547, 4554, 4555, 4557, 4574, 4575, 4577, 4744

Offset: 1

Jonathan Vos Post, Jul 21 2012

These could be called crooked numbers. Integers all of whose numerals are written (san serif) with at least one right or acute angle. The subsequence of crooked primes begins: 5, 7, 47, 457, 547, 557, 577, 757.

Exponential density 0.477... = log 3/log 10. - Charles R Greathouse IV, Jul 22 2012

Index entries for 10-automatic sequences.

Cf. A072960 (numbers using only the curved digits 0, 3, 6, 8 and 9).

A217048 Semiprimes using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

6, 9, 33, 38, 39, 69, 86, 93, 303, 309, 339, 386, 393, 398, 633, 669, 689, 698, 699, 803, 838, 866, 869, 886, 889, 893, 898, 899, 933, 939, 989, 993, 998, 3039, 3063, 3086, 3093, 3098, 3099, 3309, 3338, 3369, 3383, 3386, 3398, 3603, 3639, 3669, 3683, 3693

Offset: 1

Jonathan Vos Post, Sep 25 2012

This is to A079652 as semiprimes A001358 are to primes A000040.

			a(41) = 3338 = 2 * 1669, the 938th semiprime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A001358, A072960.

IsSemiprime:=func; [n: n in [2..3700] | IsSemiprime(n) and Intseq(n) subset [0,3,6,8,9]]; // Bruno Berselli, Sep 25 2012

R:= [0,3,6,8,9]:
Res:= NULL: count:= 0:
for m from 1 while count < 100 do
  L:= convert(m,base,5);
  n:= add(R[L[i]+1]*10^(i-1),i=1..nops(L));
  if numtheory:-bigomega(n)=2 then Res:= Res, n; count:= count+1 fi
od:
Res; # Robert Israel, Feb 16 2020

A001358 INTERSECTION A072960.

A361780 Numbers that have digits consisting only of line segments {1, 4, 7} or curved digits {0, 3, 6, 8, 9}.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 30, 31, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 60, 61, 63, 64, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 78, 79, 80, 81, 83, 84, 86, 87, 88, 89, 90, 91, 93, 94, 96, 97, 98, 99, 100, 101, 103, 104, 106, 107, 108, 109, 110

Offset: 1

Bernard Schott, Mar 23 2023

This sequence allows all digits except for 2 and 5.

Cf. A028373 (line-segment digits: {1, 4, 7}), A072960 (curved digits: {0, 3, 6, 8, 9}), A072961 (both line segments and curves digits: {2, 5}).

Cf. A082741 (digits: {1, 2, 4, 5, 7}), A028374 (digits: {0, 2, 3, 5, 6, 8, 9}), this sequence (digits {0, 1, 3, 4, 6, 7, 8, 9}).

Select[Range[0, 110], AllTrue[IntegerDigits[#], ! MemberQ[{2, 5}, #1] &] &] (* Amiram Eldar, Mar 24 2023 *)

A079653 Triangular numbers using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

0, 3, 6, 36, 66, 300, 630, 666, 903, 990, 3003, 6903, 33930, 39060, 39903, 63903, 66066, 69006, 93096, 306936, 333336, 339900, 600060, 609960, 630003, 669903, 690900, 833986, 930930, 936396, 963966, 3036880, 3069003, 3083886, 3306306, 3689686, 3966336, 3988900

Offset: 1

Shyam Sunder Gupta, Jan 23 2003

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A000217 and A072960.

t[n_] := n*(n + 1)/2; t /@ Select[Range[0, 10000], AllTrue[IntegerDigits[t[#]], MemberQ[{0, 3, 6, 8 , 9}, #1] &] &] (* Amiram Eldar, Aug 18 2020 *)

a(1) = 0 and more terms from Amiram Eldar, Aug 18 2020

A079655 Perfect squares using only the curved digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

0, 9, 36, 900, 3600, 3969, 6889, 8836, 38809, 69696, 80089, 90000, 93636, 339889, 360000, 363609, 380689, 396900, 660969, 688900, 693889, 698896, 883600, 896809, 988036, 3663396, 3869089, 3880900, 3988009, 6066369, 6086089, 6969600, 8008900, 8088336, 8803089

Offset: 1

Shyam Sunder Gupta, Jan 23 2003

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A000290 and A072960.

Select[Range[0, 3000], AllTrue[IntegerDigits[#^2], MemberQ[{0, 3, 6, 8 , 9}, #1] &] &]^2 (* Amiram Eldar, Aug 18 2020 *)

More terms from Amiram Eldar, Aug 18 2020

A079656 Cubes using only the digits 0, 3, 6, 8 and 9.

Original entry on oeis.org

0, 8, 8000, 3869893, 8000000, 3869893000, 3996969003, 8000000000, 99060039883, 339630096833, 630966396033, 688933306368, 869889903336, 3869893000000, 3996969003000, 8000000000000, 63836938680696, 99060039883000, 339630096833000, 630966396033000, 688933306368000

Offset: 1

Shyam Sunder Gupta, Jan 23 2003

Cf. A072960, A074100.

Do[ If[ Union[ Join[ IntegerDigits[n^3], {0, 3, 6, 8, 9}]] == {0, 3, 6, 8, 9}, Print[n^3]], {n, 0, 50000}]

More terms from Robert G. Wilson v, Jan 24 2003

cp's OEIS Frontend

A028374 Numbers that have only curved digits {0, 3, 6, 8, 9} or digits that are both curved and linear {2, 5}.

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A034470 Prime numbers using only the curved digits 0, 2, 3, 5, 6, 8 and 9.

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A079652 Prime numbers using only the curved digits 0, 3, 6, 8 and 9.

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A082741 Numbers that have digits consisting only of line segments or both line segments and curves (base 10 digits are 1, 2, 4, 5, 7).

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A214584 Integers whose decimal representation has only digits in {4,5,7}.

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A217048 Semiprimes using only the curved digits 0, 3, 6, 8 and 9.

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A361780 Numbers that have digits consisting only of line segments {1, 4, 7} or curved digits {0, 3, 6, 8, 9}.

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A079653 Triangular numbers using only the curved digits 0, 3, 6, 8 and 9.

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